Jelavic settled quickly at Goodison Park following his switch from Rangers in January 2012, but he has struggled for form this term and has netted just one goal in his past 18 Premier League games.
Reports suggest there are a number of clubs interested in signing the Croatian and he could be sold in the summer, but Moyes says he will not be going anywhere.
"His effort has never been in question and we'd want him here next year," said the Everton boss.
"It's been a difficult season - maybe a bit of second-season syndrome.
"He's found it a little harder to get the goals and the opportunities.
"We kept trying to play him to give him the chance to score but in the end we had to take him out. As it is, Victor Anichebe has come to light in the last month or so which has given us a wee bit of something else."
Moyes accepts that Jelavic's morale has suffered as a result of his poor form but believes he has the strength of character to bounce back.
He said: "His confidence has taken a bit of a knock. If you've not scored and not played as well that's natural.
"He's a good lad and he's the first one to accept he's not doing well enough.
"When you work with boys like that it makes it a lot easier because they know they have got to get better."